Who invents the axioms?

During an interesting discussion amongst friends at Synagogue on Saturday about the nature of knowledge, talk inevitably turned to Gödel's Incompleteness Theorem (inevitable because I was chatting to a bunch of geeks). Wikipedia tells me there are two such theorems (who knew?).

Ari Trachtenberg, a BU scientist, piped in that "for mathematics, we invent the axioms. In science, God invents them, and we work on discovering them."

I think that is an excellent distinction, and it may be extensible to a discussion on unsustainability. In industrial agriculture we invent the axioms, in nature, God invents them.

What happens when we try to create an agriculture such as at Polyface Farm, as described so beautifully in Michael Pollan's book, The Omnivore's Dilemma, in which we harness nature rather than fight it. I think this is science at its best: discovering God's axioms.

While you can, and if you haven't, please go ahead and sponsor Hannah or me for the Hazon 2006 New York Bike ride.

Technorati: axioms unsustainability sustainability mathematics science agriculture Polyface Farm